Background/Question/Methods
There is a longstanding debate whether omnivory stabilizes or destabilizes population dynamics. Recent studies suggest that the stability or instability of omnivorous interactions depends on the specific biological rates of metabolism and consumption as well as the preference for a prey species and that anything is possible when these parameters are chosen at random. However, the metabolic theory of ecology showed that the biological rates are neither random nor independent. Instead, these parameters follow three-quarter power-law relationships with individual body mass. Additionally, foraging theories demonstrated that the preferences (i.e. relative interaction strengths) of polyphagous predators with their multiple prey follow hump-shaped relationships with the predator-prey body-mass ratios with a peak at intermediate or optimal body size ratio. Implementing these two theories, we used a bioenergetic population dynamic model to analyze the dynamical behavior of the tri-trophic food chains with or without omnivory..

Results/Conclusions
We found that (1) co-existence of species is only possible at specific body-mass ratios, (2) omnivorous links stabilize population dynamics and increase species persistence, and (3) top-predators with small optimal body-mass ratios are only persistent in tri-trophic food chains, whereas top predators with large optimal body-mass ratios gain stability by omnivorous interactions. Our results suggest that omnivorous interactions in natural food webs may be stabilized by metabolic and foraging constraints imposed by the body masses of predator and prey species. This helps reconciling the longstanding debate on the consequences of omnivory for the stability of complex natural food webs.